Main interests:
- Algorithmic information theory (algorithmic probability and universal distribution)
- Pure NKS research
- Real computation
Trying to found 2 new fields from merging NKS and experimental mathematics
with algorithmic information theory and meta-mathematics:
Other research interests:
On hermeneutics:
- From von Kempelen to von Neumann on inteligent machines
- From Descartes to de La Mettrie on the human being as a machine
- From Suarez and Grosseteste to Cantor on infinity
- From Leibniz to Turing on universality
- From Euclid to Hilbert on axiomatisation
Contemporary authors of my interest: Wolfram, Chaitin, Gödel, Kolmogorov, Levin on complexity, randomness and irreducibility.
Other:
- Computational Linguistics
- Math data collections (axioms, notations, symbols)
- Automatic theorem proving and proof visualization
- History of writing and language
- Literature (Alfonso Reyes, Jorge Luis Borges, Douglas Hofstadter, Umberto Eco)
Contemporary favorite books:
- A New Kind of Science, Stephen Wolfram
- Computation, Finite and Infinite Machines, Marvin Minsky
- The Computational Beauty of Nature, William Flake
- Cellular Automata, Illachinsky
- Gödel, Escher and Bach, Douglas Hofstadter
- Whom the Gods Love: The Story of Evariste Galois, Leopold Infeld
Ancient favorite books:
- Elements, Euclid
- Euclid Vindicatus; Saccheri
- Elements of Geometry, Legendre
- L'homme comme machine, de La Mettrie
- Discours de la méthode, Descartes
- Discours de metaphysique, Leibniz
- Monadology, Leibniz
